Finding the Area of a Sector using Trigonometric Functions

  • Thread starter Thread starter chwala
  • Start date Start date
  • Tags Tags
    Area
AI Thread Summary
The discussion focuses on calculating the area of a sector using trigonometric functions, specifically addressing part (c) of a problem. One participant shares their solution, arriving at an area of approximately 80.84 cm² using the sine function. Another participant suggests an alternative approach using the cosine function, noting its relation to the sine of 1 radian. A minor correction is made regarding the area calculation, adjusting it to 80.83 cm². The conversation highlights different methods for solving the same problem in trigonometry.
chwala
Gold Member
Messages
2,825
Reaction score
413
Homework Statement
See attached
Relevant Equations
Area of sector
My interest is on part (c) only.

1648079111365.png


Wow, this was a nice one! boggled me a little bit anyways; my last steps to solution,
##A= \dfrac{1}{2} ×16.8319^2 × 0.5707=80.84cm^2## bingo!
Any other approach apart from using sine?
Cheers guys
 
Physics news on Phys.org
chwala said:
Any other approach apart from using sine?

Yes ! Using the cosine of angle FEH (which happens to be the sine of 1 radian, but that may well be a coincidence :smile: )

Your calculator needs new batteries: not 80.84 but 80.83 :wink: !

##\ ##
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Similar threads

Find area of the shaded part in the given diagram
Replies
2
Views
2K
Find the Area of the shaded region in the given problem
Replies
1
Views
1K
Trigonometry: finding an angle, area and length of sector of a circle
Replies
2
Views
2K
Solve the quadratic equation involving sum and product
Replies
2
Views
2K
Find the possible values of angle ##∠ADB##
Replies
2
Views
1K
Solve the quadratic equation that involves sum and product
Replies
1
Views
2K
Find Co-ordinates of Point C in Problem Involving Straight Line Equations
Replies
2
Views
1K
Find the surface area of the water in the given prism
Replies
3
Views
2K
Find the area of the quadrilateral OCBAO
Replies
8
Views
1K
Prove the trigonometry identity and hence solve given problem
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top